It is known that IQ\'s obtained from a standard IQ test are normally distributed

Question

It is known that IQ's obtained from a standard IQ test are normally distributed with an average IQ of 100 and a standard deviation of 12. About what percentage of the population has an IQ greater than 94 but less than 109? 38% 46% 55% 93% What is the approximate score corresponding to the 85th percentile? 185 112 118 85 A fair coin is tossed 6 times. Two possible sequences of results are (i) HTTHTH or (ii) HHHHHH. Which of the following statements is correct. Sequence (i) is more likely. Sequence (ii) is more likely. Both sequences are equally likely. Which one of the following P-values most strongly suggests that the null hypothesis is true? 4% 4% 14% 34%

Explanation / Answer

given mean = 100 standard deviation =12

6) percentage of population greater than 94 less than 109

we know that z formulea = z= x^- u / standard devaition

so p(x <109<x > 94) =

p(x<109 ) = (109- 100) / 12 = 0.75

from standard z table value of 0.75 = 0.7734

p(x>94 ) = 1-p(x<94) = [ 94-100] / 12 = 6/12 = -0.5

from standard z table value of -0.5 = 0.3085

  p(x <109<x > 94) = 0.7734-0.3085 =0.4649 = 46.49%

option b

7 ) 85th percentile

z =( 85-100) / 12 = -15/12=-1.25

pvalue from standard z table = 0.1056 =105.6%

8)

HTTHTH OR HHHHHH

WHEN A COIN TOSSED 6 TIMES

when a coin is tossed u may get head or tail so its not always possible to get head all time and tail all time

so option c) both sequences are equally likely

9)

a) p value 0.4% 0.004 = 0.5000

b) p value 4% 0.04 = 0.5610

c) pvalue 14% 0.14 = 0.5557

d) p value 34& 0.34= 0.6331

so from this option a null hypothesis h0 : 0.5

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